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# Applying the Probability Model

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Please see attached files and use it to apply the questions if needed:

1) The definition of a probability model. Illustrate the two parts of the definition with an example selected from the worksheet.

2) Define the notion of independent events in a probability model. Using as your model the 36 element set of outcomes obtained by tossing two fair dice, let A be the event that the first die comes up even and B the event that the sum of what's showing on the two dice is equal to 7. Are A and B independent?

3) If an ice cream shop sells 4 flavors of ice cream, assuming that all orders of two scoops are equally likely, what is the probability that in an order of two scoops both are of the same flavor? Hint: When you calculate the "numerator", treat the two stars as a single letter. (PG. 6-7)

4) Briefly summarize the experimental design for deciding whether a proposed treatment should go on for further study. Note where independence came into play. If you were more conservative and reject the treatment only if the probability that it is 30% effective is less than .05 what does the math tell you about whether you would more than 14 patients or fewer than 14 patients? (PG.9)

##### Solution Summary

Combinatorial formulas and probability rules. Checking whether two events are independent of not.

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###### Education
• BSc, University of Bucharest
• MSc, Ovidius
• MSc, Stony Brook
• PhD (IP), Stony Brook
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